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XL1Y. On the Law of Atomic Weights. 

 [Plate IV.] 

 To the Editors of the Philosophical Magazine. 

 Gentlemen, 



IX 1888 I submitted to the Royal Society a paper on the 

 Law o£ Atomic Weights, in which it was shown that 

 the succession of atomic weights, when arranged as in Men- 

 deleeff's table, follows two nearly coincident laws — one of 

 which, if fully ascertained, would furnish the atomic weights 

 of the artiads or elements of even atomicity ; and the other, 

 of the perissads or elements of odd atomicity. 



The cause why atomic weights obey these laws is not 

 known ; but the fact that they do obey them can be estab- 

 lished, and it is to be hoped that the much greater discovery 

 of the cause of these laws will follow. 



Exceptional difficulties, however, present themselves in the 

 way of man's study of the cause, for reasons which are ex- 

 plained in the paper above referred to ; and meantime we 

 can only gain some knowledge of the laws empirically, i.e., 

 by finding whether definite equations, or definite curves, will 

 furnish values for the atomic weights which lie within, or 

 nearly within, the limits of the probable errors of the best 

 determinations that have been made experimentally. By a 

 definite curve is meant one which is not made up of portions 

 of different curves put together, but is itself, and throughout 

 its whole length, a single curve capable of being represented 

 analytically by a single equation. 



Each of the laws referred to in the first paragraph might 

 be adequately represented in a diagram by the positions in 

 which a slightly sinuous curve intersects equidistant vertical 

 lines representing the successive steps of the Mendeleeff 

 series, and it was shown that the two curves of this kind be- 

 longing respectively to the artiads and perissads, lie everywhere 

 close to a simpler curve without sinuosities, which can be 

 represented analytically by a very simple equation, and which 

 we may call the central curve. 



Accordingly another and convenient way of representing 

 the facts ^grammatically is to take the positions in which 

 this simpler curve intersects the equidistant vertical lines, 

 and to apply to these positions one set of deviations for the 

 artiads and another set of deviations for the perissads. It 

 was found that this central curve may be either a logarithmic 

 curve or an elliptic curve. These curves lie so close to one 

 another throughout that part of their length of which it was 

 neces.-arv to make use, that either will answer, provided that 



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